Solving the Linear Equation: 3ax + b = c

In the world of high school mathematics, one of the fundamental skills students must master is the ability to solve linear equations. These equations, which take the form of 3ax + b = c, where a, b, and c are constants, are crucial for understanding and applying mathematical concepts in various real-world scenarios.

Step 1: Isolate the Variable

The first step in solving the equation 3ax + b = c is to isolate the variable x on one side of the equation. To do this, we need to perform the necessary operations to "undo" the coefficients and constants that are multiplying or adding to the variable.

1. Subtract b from both sides: 3ax + b - b = c - b
2. Simplify: 3ax = c - b

Step 2: Divide Both Sides by the Coefficient of x

Now that we have the variable x isolated on one side of the equation, we need to divide both sides by the coefficient of x, which in this case is 3a.

1. Divide both sides by 3a: (3ax) / 3a = (c - b) / 3a
2. Simplify: x = (c - b) / (3a)

The Final Solution

The final solution to the equation 3ax + b = c is:

x = (c - b) / (3a)

This formula allows us to find the value of x by substituting the known values of a, b, and c into the equation.

It's important to note that this process can be applied to any linear equation in the form 3ax + b = c, regardless of the specific values of a, b, and c. The key is to follow the same systematic steps of isolating the variable and then dividing both sides by the coefficient of the variable.

By mastering this technique, high school mathematics students can confidently tackle a wide range of linear equations, laying a strong foundation for more advanced mathematical concepts and problem-solving skills.